Question

at sangers auto garage, 40% of the cars brought in for service need an oil change. of the cars that need oil change, 30% also need a tire rotation find the probability that a car that comes into the auto garage needs both an oil change and a tire rotation

Answer 1

3/10

Answer 2

If we let O = event that a car needs an oil change = 40% = 0.40
We will let (T|O) = event that a car needs a tire rotation, given that it has had a tire change already = 30% = 0.30

So we are looking for the probability that a car needs both or P(O 'intersection' T), then by conditional probability:

\[P(O 'intersection' T) = P(O|T)P(T) = P(T|O)P(O)\]

So, as P(T|O) = 0.30, P(O) = 0.40, this problem can be solved by multiplication.

Answer 3

We need both conditions, so multiply the probabilities. I would think the answer would be about .12 or 12 percent.